Ultimate dynamics and optimal control of a multi-compartment model of tumor resistance to chemotherapy
A. Alvarez-Arenas, K.E. Starkov, G. F. Calvo, Juan Belmonte-Beitia
Discrete and Continuous Dynamical Systems B 24(5) 2017-2038 (2019)
In this paper, a non-trivial generalization of a mathematical model put forward in [35] to account for the development of resistance by tumors to chemotherapy is presented. A study of the existence and local stability of the solutions, as well as the ultimate dynamics of the model, is addressed. An analysis of different chemotherapeutical protocols using discretization and optimization methods is carried out. A number of objective functionals are considered and the necessary optimality conditions are provided. Since the control variable appears linearly in the associated problem, optimal controls are concatenations of bang-bang and singular arcs. A formula of the singular control in terms of state and adjoint variables is derived analytically. Bang-bang and singular controls from the numerical simulations are obtained where, in particular, singular controls illustrate the metronomic chemotherapy.